Newton polygons of L-functions associated to Deligne polynomials

Newton Polygons and Families of Polynomials

We consider a continuous family (fs), s ∈ [0, 1] of complex polynomials in two variables with isolated singularities, that are Newton non-degenerate. We suppose that the Euler characteristic of a generic fiber is constant. We firstly prove that the set of critical values at infinity depends continuously on s, and secondly that the degree of the fs is constant (up to an algebraic automorphism of...

Higher Order Bernoulli Polynomials and Newton Polygons

VARIATION OF p -ADIC NEWTON POLYGONS FOR L-FUNCTIONS OF EXPONENTIAL SUMS

Abstract. In this paper, we continue to develop the systematic decomposition theory [18] for the generic Newton polygon attached to a family of zeta functions over finite fields and more generally a family of L-functions of n-dimensional exponential sums over finite fields. Our aim is to establish a new collapsing decomposition theorem (Theorem 3.7) for the generic Newton polygon. A number of a...

Coefficient functions of the Ehrhart quasi-polynomials of rational polygons

In 1976, P. R. Scott characterized the Ehrhart polynomials of convex integral polygons. We study the same question for Ehrhart polynomials and quasi-polynomials of nonintegral convex polygons. Define a pseudo-integral polygon, or PIP, to be a convex rational polygon whose Ehrhart quasipolynomial is a polynomial. The numbers of lattice points on the interior and on the boundary of a PIP determin...

Erratum to: Newton polygons and curve gonalities

We have made a conceptual error in the construction of our regular strongly semistable arithmetic surface X over C[[t]], as explained in [2, Sect. 7]. The error lies in the last part, involving toric resolutions of singularities. Namely, it has been overlooked that the exceptional curves that are introduced during the resolution may appear with non-trivial multiplicities, turning X non-stable. ...